"Isn't that the lesson in the book of Jonah--you can't hide from God because God is everywhere?"

Er, NO. The particular 'lesson' in Yonah is in the last verses of the story, where YHVH tells Yonah that He(YHVH) cares about the people of Ninevah, too (who were assuredly pagans and not Israelites). At least for me, that's the 'punch line' of the entire book.

Reading it as an adult, I agree. "You can't hide from God because God is everywhere" is the moral I took the story to have when I heard it as a child. Perhaps that was emphasized in the way it was told to me (I remember a children's picture version with very colorful illustrations and almost rhyming language), or perhaps it's that the whole idea of prophecy and God destroying a city went right over my head, but that silly Jonah tried to run away from God and it didn't work was an idea I could grasp. I remember that as the first I ever really heard of the "God is everywhere" concept.